1. Field of the Invention
The present invention relates to a three-dimensional photonic crystal including a three-dimensional refractive index periodic structure and to a functional device including the three-dimensional photonic crystal, such as for example an optical waveguide, an optical resonator, an optical filter, and a polarizer.
2. Description of the Related Art
Yablonovitch has proposed the concept that the transmission and reflection characteristics of an electromagnetic wave can be controlled using a structure smaller than the wavelength of the electromagnetic wave (Physical Review Letters, Vol. 58, pp. 2059, 1987). According to this document, the transmission and reflection characteristics of the electromagnetic wave can be controlled with a periodic structure smaller than the wavelength.
In particular, when the wavelength of electromagnetic waves is reduced to about the wavelength of visible light, transmission and reflection characteristics of the visible light can be controlled. Such a structure is known as a photonic crystal. It has been suggested that a reflecting mirror having a reflectance of 100% in a certain wavelength region can be manufactured.
Thus, a certain wavelength range in which a reflectance of near 100% can be realized may be referred to as a photonic band gap, as compared to the energy gap in a semiconductor.
Furthermore, a three-dimensional fine periodic structure can provide a photonic band gap for incident light from any direction. This is hereinafter referred to as a complete photonic band gap.
The complete photonic band gap can have various applications (for example, reduced spontaneous emission in a light-emitting device). A structure that can achieve a complete photonic band gap in a wider wavelength region can facilitate extending the operating wavelength region of such a functional device.
Some structures having a complete photonic band gap have been proposed (see for example U.S. Pat. Nos. 5,335,240, 5,440,421, and 6,597,851).
FIG. 14A shows a woodpile structure proposed in U.S. Pat. No. 5,335,240. In this structure, a plurality of columnar structures disposed in parallel are stacked, the alignment of each layer rotated by 90 degrees with respect to that of adjacent layers.
FIG. 14B is a schematic view of a structure exhibiting a photonic bandgap disclosed in U.S. Pat. No. 5,440,421. In this structure, a plurality of holes have been made in a direction perpendicular to a plurality of columnar structures that are disposed in parallel so that parts of the columnar structures overlap in the stacking direction.
FIG. 14C is a schematic view of a structure exhibiting a photonic bandgap disclosed in U.S. Pat. No. 6,597,851. In this structure, layers having holes provided in the form of a triangular lattice and columnar structures provided in the form of a triangular lattice are stacked with a shift of ⅓ of the fundamental period between adjacent layers.
In the woodpile structure disclosed in U.S. Pat. No. 5,335,240, since four layers constitute one period, the structure is simple and is easily produced. However, the structure has a strong anisotropy, resulting in a strong directional dependence of the photonic bandgap.
The structure disclosed in U.S. Pat. No. 5,440,421 also has a complete photonic bandgap. However, a plurality of very deep holes must be formed, and it is very difficult to produce the structure.
The structure disclosed in U.S. Pat. No. 6,597,851 has an anisotropy smaller than that of the woodpile structure and has a relatively large photonic bandgap. However, since six layers constitute one period, the fabrication process is complex, for example, high accuracy is necessary for the alignment of layers. Thus, it is difficult to produce the structure.